点元表示的参数曲面相切判断与计算

摘要

A novel tangent detection and calculation algorithm is presented for parametric surfaces based on discrete surfels. The two surfaces are initially uniformly sampled into surfels.Surfels of each surface are then organized into a space octree with surfels' normal bounding cones being built at each octree node. By checking the consistency of the normal bounding cones together with the enclosing box test, the algorithm can detect the potential tangent area between the two surfaces robustly. The candidate surfels are resampled at high resolution to ensure the accuracy of the result and then tangent operation is carried out at last. Experiments show that the algorithm is effective and easy to implement by analyzing possible tangent area to find tangent points within the error range.%提出了一种基于点元的参数曲面求切新算法,该算法先对曲面进行离散点元采样,通过层次包围盒测试,建立法向包围锥,对判断为可能相切的区域,根据精度自适应动态重采样点元,最后进行求切运算.实验表明,通过对曲面可能相切区域分析检测,能够针对曲面相切的情况在可控误差范围内有效求出切点,算法稳定可靠且易于交互.